Some of the matrix manifolds we consider
(such as symmetric, triangular, tridiagonal or circulant)
can be phrased as linear equality constraints and can, in principle, be solved
with linear-equality constrained least squares [1]}.
However, the number of equality constraints needed is \(\mathcal {O}(n^2)\) 
so the resulting least squares matrix will have \(\mathcal {O}(n^2)\)  rows,
which is intractably large in most applications.
Thus, we avoid phrasing the piDMD constraints in terms of linear equality constraints and instead
exploit properties of the matrix manifold to find solutions that can be efficiently implemented
(see sections REF  and REF , for example).
